﻿//-----------------------------------------------
//
//	This file is part of the Siv3D Engine.
//
//	Copyright (c) 2008-2025 Ryo Suzuki
//	Copyright (c) 2016-2025 OpenSiv3D Project
//
//	Licensed under the MIT License.
//
//-----------------------------------------------

# include <Siv3D/PrimeNumber.hpp>
# include <boost/multiprecision/cpp_int.hpp>

namespace s3d
{
	////////////////////////////////////////////////////////////////
	//
	//	IsPrime
	//
	//	Forišek, Michal, and Jakub Jancina. 
	//	"Fast Primality Testing for Integers That Fit into a Machine Word⋆." (2015).
	//
	////////////////////////////////////////////////////////////////

	namespace detail
	{
		static constexpr uint16_t bases32[] = { 15591,2018,166,7429,8064,16045,10503,4399,1949,1295,2776,3620,560,3128,5212,
			2657,2300,2021,4652,1471,9336,4018,2398,20462,10277,8028,2213,6219,620,3763,4852,5012,3185,
			1333,6227,5298,1074,2391,5113,7061,803,1269,3875,422,751,580,4729,10239,746,2951,556,2206,
			3778,481,1522,3476,481,2487,3266,5633,488,3373,6441,3344,17,15105,1490,4154,2036,1882,1813,
			467,3307,14042,6371,658,1005,903,737,1887,7447,1888,2848,1784,7559,3400,951,13969,4304,177,41,
			19875,3110,13221,8726,571,7043,6943,1199,352,6435,165,1169,3315,978,233,3003,2562,2994,10587,
			10030,2377,1902,5354,4447,1555,263,27027,2283,305,669,1912,601,6186,429,1930,14873,1784,1661,
			524,3577,236,2360,6146,2850,55637,1753,4178,8466,222,2579,2743,2031,2226,2276,374,2132,813,
			23788,1610,4422,5159,1725,3597,3366,14336,579,165,1375,10018,12616,9816,1371,536,1867,10864,
			857,2206,5788,434,8085,17618,727,3639,1595,4944,2129,2029,8195,8344,6232,9183,8126,1870,3296,
			7455,8947,25017,541,19115,368,566,5674,411,522,1027,8215,2050,6544,10049,614,774,2333,3007,
			35201,4706,1152,1785,1028,1540,3743,493,4474,2521,26845,8354,864,18915,5465,2447,42,4511,
			1660,166,1249,6259,2553,304,272,7286,73,6554,899,2816,5197,13330,7054,2818,3199,811,922,350,
			7514,4452,3449,2663,4708,418,1621,1171,3471,88,11345,412,1559,194 };

		static constexpr uint32 bases64[] = { 2404423, 3027617, 3715179, 3264583, 1593555, 5853461, 1552463, 1896881, 2904107, 5600043,
			1356087, 2044251, 290821, 1150981, 1642719, 3076389, 667689, 2650251, 1200327, 1724421, 4133355, 4494151,
			1151005, 2674735, 2404773, 667731, 249897, 2904087, 1257551, 1298703, 815165, 241669, 987333, 1839543,
			1101997, 151581, 2216193, 3314043, 3387621, 1503569, 1569019, 2674851, 2429437, 2798241, 1380357, 421955,
			2330647, 1716501, 1101973, 2757207, 1200199, 3395643, 987153, 1257519, 2945595, 1994825, 1642879, 1716607,
			1470537, 274473, 5034585, 2707899, 741477, 2871903, 323643, 1052677, 1503513, 1110213, 3371237, 864345,
			5157741, 2830397, 4723085, 1896521, 3518631, 913487, 2674725, 1274089, 1445893, 397317, 2650461, 462937,
			2535471, 815171, 1150993, 299037, 1675281, 2011285, 1273861, 2281743, 290821, 4305755, 1552533, 2945205,
			1282185, 2625573, 339999, 1028275, 1429797, 217093, 4133591, 1110033, 3150567, 1913109, 274445, 3322029,
			1995003, 1527957, 954595, 979071, 446495, 1896509, 987327, 1642501, 3617519, 733323, 979101, 3314187,
			1298503, 2535857, 1642555, 1052715, 3371339, 4084005, 1445941, 782425, 979047, 1200307, 1527851, 1888713,
			2084869, 618609, 1552551, 520199, 1052865, 987141, 1527935, 1052679, 1593367, 1028323, 815117, 913421,
			1159239, 1445929, 2584925, 1200391, 929895, 1839183, 1642585, 1888263, 979071, 364617, 520301, 4133525,
			4714863, 3510373, 3535449, 2281935, 790629, 1724799, 3363279, 3150287, 1355829, 2043957, 4059165, 569475,
			1888603, 618627, 274485, 1028233, 667695, 274463, 1626363, 3100901, 2454075, 217129, 397335, 1298485,
			806915, 1110087, 1151085, 1642569, 4182525, 413733, 2085231, 1028289, 987285, 1200265, 569397, 438331,
			1896587, 2797941, 618507, 913599, 2281475, 1282221, 3518661, 3002625, 1896453, 1896699, 1101987, 4059263,
			1913059, 3617157, 2454007, 1200339, 299069, 2626077, 1134611, 1273917, 1569025, 3265155, 3535675, 1151059,
			3494019, 3494345, 978987, 299019, 2429415, 864453, 1798247, 2339057, 323607, 2060727, 6836295, 1773669,
			667721, 1839547, 978949, 667661, 1101933, 1200169, 3879775, 2241021, 2216177, 2699611, 1446181, 1593397,
			3371121, 684139, 684073, 806949, 2281845, 733273, 1446001, 618519, 1839231, 2633837, 4223419, 4297153,
			438315, 2240823, 2428989, 462901, 618555, 3715119, 438303, 1077307, 938115, 987239, 782349, 4969091,
			1593457, 2306547, 2404357, 1675311, 1101937, 4084065, 708661, 2330815, 1200187, 1257485, 979125, 274485,
			1724723, 3002789, 1274127, 2044187, 1675277, 2461979, 1101855, 4304957, 1765567, 2625777, 2011143, 1593555,
			790541, 1028197, 741429, 462957, 2404575, 2084977, 5575515, 790685, 1110227, 1200327, 3903601, 806979,
			3494579, 1298605, 2240541, 790635, 741435, 1527935, 4518067, 4543533, 2134083, 1724429, 1675661, 3732063,
			2830617, 2510909, 1134773, 1962445, 1298511, 3026991, 4453085, 2535867, 4174311, 4133451, 1028293, 1470775,
			3313971, 2453523, 610387, 1888353, 561279, 2536025, 1134615, 2216019, 790545, 1298449, 4026715, 782445,
			1470715, 2339027, 569475, 708619, 2011495, 667757, 3395825, 1962235, 790559, 1568805, 815285, 2527335,
			3002807, 2142359, 1626285, 987177, 2707569, 790533, 2535573, 462901, 1568949, 2486379, 741507, 4837755,
			929821, 1257755, 2757255, 561265, 1200225, 413719, 1552415, 2486375, 5624007, 1798575, 3395985, 929835,
			1356005, 684115, 290875, 4477317, 667715, 364575, 4518139, 864455, 1028295, 1765413, 3510781, 1028115,
			4796747, 1380411, 1421643, 2945413, 1110045, 1052689, 1724817, 2306229, 3837963, 987173, 2699643, 151559,
			1814631, 2871957, 708679, 815271, 979045, 1200229, 2699545, 3043441, 2216193, 3437035, 3150023, 3371087,
			249899, 4174821, 5255517, 4026909, 1528001, 643115, 1151055, 2626155, 4714999, 3510631, 1110195, 2904137,
			167949, 1528049, 94225, 8655567, 913467, 151575, 1626291, 1814769, 2625549, 339981, 241707, 2625693,
			2216165, 2535591, 126989, 2584689, 1028253, 5337521, 1421439, 561205, 2134503, 1380581, 1052709, 6189349,
			4059755, 2535887, 864365, 667721, 2338953, 3879193, 2306197, 1716307, 2453773, 815283, 1110179, 3494699,
			2707713, 3076599, 618557, 1552487, 2510927, 1814929, 6608415, 1101981, 2585177, 5239611, 1503455, 217135,
			1200277, 667651, 290877, 2461823, 5656589, 929919, 2134495, 446487, 3003077, 1380383, 2486315, 1642669,
			340009, 2871607, 2404791, 1593613, 2142561, 1995201, 4469545, 1888489, 4174647, 2011347, 2011239, 913557,
			1765503, 3436587, 1028259, 1101891, 5035137, 2085343, 1814709, 2650755, 1503413, 3535041, 815261, 815211,
			3396341, 249869, 323601, 2134243, 667653, 1298473, 569347, 2773665, 954541, 2625849, 2281873, 3634015,
			733255, 3117393, 1110273, 217111, 913619, 5403577, 864297, 1356053, 2535933, 2626105, 2281581, 1765539,
			2404621, 1814791, 3437271, 1052683, 2584815, 1134833, 421967, 930015, 1134611, 2634065, 274469, 176141,
			2871897, 2404525, 340047, 1355847, 1552607, 1593525, 864323, 790595, 2330887, 1200181, 782503, 1200319,
			684061, 2011315, 1274067, 1110207, 397317, 1282341, 1421353, 1282155, 667785, 1298445, 1675371, 5042277,
			1150989, 782403, 1724445, 462877, 2945631, 1052685, 2674915, 979003, 684091, 2363529, 1773605, 4600667,
			3961505, 3608713, 6435735, 5828901, 2461935, 1642563, 954477, 815285, 1503333, 569481, 2699763, 77837,
			1159367, 4223115, 1839315, 4379103, 1273879, 864285, 2773261, 4001839, 954411, 1052809, 1765387, 1134597,
			2633985, 3002411, 2699391, 438285, 1356053, 1470573, 1839477, 2584787, 1912863, 1626221, 1724817, 3100739,
			3535509, 929971, 1159271, 421893, 2535591, 1994925, 2240735, 1421581, 643185, 421955, 1896557, 643155,
			1503291, 2240705, 2486523, 1355859, 1569115, 1503383, 1896579, 1282157, 1716405, 3076559, 2339199, 1028109,
			2044155, 1642879, 618605, 1896785, 2584965, 1052811, 1552445, 643169, 1994925, 520197, 2134329, 1798527,
			2306187, 1962381, 1568917, 1814545, 5329665, 1380591, 4723485, 1503389, 3396185, 1675487, 5313729, 938093,
			864339, 2510945, 1716465, 1282121, 2650263, 1274113, 2756619, 1724421, 815235, 1765669, 1773605, 3535207,
			2404501, 3617445, 1896561, 1159269, 3436795, 2142287, 3363429, 1552565, 5328927, 3838305, 913607, 3879709,
			1110209, 1445995, 4059777, 1995003, 1675403, 667805, 2330653, 2756865, 815285, 782377, 1445917, 1101921,
			413709, 1446165, 3764765, 4231941, 913571, 2216043, 2625549, 2585055, 1814707, 1716555, 2306437, 1273873,
			2363703, 3805911, 1052923, 4256267, 2281821, 397329, 864365, 2634041, 1470745, 2339213, 1552413, 2871957,
			1200141, 4452915, 913565, 790631, 2043965, 1028179, 1101955, 3395691, 3314383, 4887567, 1675395, 741449,
			1429661, 1298463, 536637, 1839127, 1568917, 421901, 1888603, 2797989, 782515, 610365, 4354071, 1913071,
			2453547, 1028175, 938111, 1134821, 397317, 1675311, 1626381, 2240745, 610333, 1888315, 4297581, 1675283,
			1569061, 1724649, 1421509, 1798191, 290875, 397401, 397401, 2633979, 1814791, 3223709, 807075, 3027575,
			1773819, 3166249, 4600847, 954435, 3117069, 1200355, 2699767, 1101861, 1298671, 438303, 3322443, 1593625,
			913481, 1675391, 4026705, 1995083, 790551, 1675661, 1765689, 1200217, 2134299, 741479, 2085027, 1470757,
			438345, 2011399, 2363649, 815177, 2134465, 3002831, 1839135, 1593675, 913589, 1159187, 2363835, 741381,
			1028245, 733225, 5231149, 667689, 864269, 217117, 3387501, 2699497, 569445, 446565, 1052719, 536617,
			569481, 3855159, 438325, 1716307, 118803, 1675463, 3396063, 1429635, 4887547, 3764229, 1150987, 987243,
			3395693, 954471, 299051, 1298599, 1429841, 2708057, 3510655, 2978369, 274443, 1626471, 2240525, 733189,
			1626275, 2904671, 5354439, 1593357, 1052709, 3371207, 413733, 2338973, 1028253, 1593607, 569445, 979173,
			1101855, 4985961, 1257753, 176141, 3879411, 2511297, 1134759, 815271, 938015, 2699697, 1724439, 1052865,
			1429817, 864383, 3076805, 1257665, 1913043, 1134785, 938091, 733189, 1839451, 53251, 536703, 2339247,
			5042483, 4624893, 3223589, 2085325, 520293, 806925, 3166441, 4599975, 3387433, 954559, 3765083, 1159445,
			1028127, 643091, 1445893, 3027323, 1421589, 4133057, 3617001, 2044197, 2527329, 3117747, 4027251, 4796649,
			1839277, 3617429, 3961505, 1052761, 3363205, 69643, 708711, 1995003, 1716555, 2527471, 4354227, 782343,
			561235, 1298595, 2871369, 2650611, 913455, 1470517, 1052901, 790541, 2904107, 2650165, 643085, 790531,
			1503465, 1421629, 1765513, 2281575, 3027083, 323627, 6788253, 3764313, 2044185, 2429259, 1675535, 1274133,
			2281479, 2363465, 1642509, 1151215, 2216135, 2945173, 1445997, 1052799, 2527581, 1872321, 1593405, 421967,
			1798185, 1028329, 217105, 987365, 2011449, 1675461, 2331091, 954429, 561195, 815157, 667757, 618645,
			667749, 1593349, 2511449, 2339295, 1446085, 610405, 1593661, 118801, 3002931, 2461827, 979041, 5328963,
			1994943, 1765605, 2871837, 1355817, 2453727, 1896891, 1151127, 2486793, 1552607, 618585, 3592271, 192517,
			1200351, 5869861, 2535675, 1380581, 3002789, 1798475, 274445, 2511111, 462945, 1675283, 4231521, 2461889,
			913539, 4920173, 1159251, 5230815, 249903, 3043375, 3043375, 3314425, 1871961, 290875, 3002871, 1052785,
			2945467, 1896479, 2363429, 937997, 1569037, 569405, 3002877, 2650375, 4083779, 3043501, 1503585, 643211,
			1028199, 1110057, 2429221, 979143, 2462139, 2281543, 1765735, 2773231, 6321299, 1134863, 3960837, 3166617,
			569349, 3608769, 3117115, 3314311, 2674785, 2871559, 1568847, 1872021, 1642539, 913451, 2043947, 1421595,
			667751, 1888405, 1356045, 1912845, 1839375, 438301, 4149861, 1503429, 1552665, 1527989, 5255359, 864269,
			2634305, 5066951, 3510471, 2281975, 3322595, 2674693, 2527653, 2486303, 536679, 2675131, 2527515, 1110099,
			2240823, 782349, 3363535, 3764277, 1716481, 3314037, 1429677, 3387565, 1282215, 643109, 2650305, 3100979,
			4763755, 733189, 987273, 2773623, 1642647, 2060451, 2978411, 126999, 1593717, 643115, 3264931, 2453755,
			2584803, 3224061, 2773221, 1896687, 4231215, 2330803, 618645, 1626351, 2535527, 2511425, 3396323, 2281831,
			7467699, 1642575, 2650115, 413775, 1527813, 2044071, 815241, 782437, 3731469, 4174581, 192525, 3387649,
			618569, 987179, 4862781, 1134651, 2142699, 1503459, 2142491, 2281503, 6346163, 3633939, 815255, 2699613,
			979045, 2757267, 790595, 1110245, 2707913, 979167, 3494429, 7278965, 3076433, 2674759, 217111, 438313,
			1200141, 3150093, 192517, 3117499, 1102053, 2216109, 913607, 3617045, 1724483, 1552421, 1527813, 1724517,
			741525, 733281, 807043, 536629, 1839231, 2486535, 1913071, 1913095, 364617, 1282239, 1642695, 5870031,
			167959, 1446157, 2633961, 1446201, 413793, 1552523, 2060559, 3960837, 3592301, 913439, 2216127, 741527,
			4886629, 118807, 2044301, 1257561, 2626137, 2650153, 299045, 790659, 1257653, 806953, 1282341, 610307,
			2085223, 3494117, 364567, 3002375, 3510513, 5239553, 2871435, 3879709, 1380533, 733291, 2797969, 2650659,
			1159307, 618501, 913565, 1134803, 2060299, 1765473, 938195, 1871913, 2536001, 913419, 1896837, 1298659,
			1200391, 1814757, 2085285, 2650753, 1962343, 3838749, 2084869, 1773581, 684091, 1429541, 2634215, 1888563,
			561163, 733225, 3150425, 1503545, 1888269, 1028245, 3321945, 6140731, 2428975, 2773651, 3731647, 69645,
			3150213, 1765615, 4174401, 1552731, 561283, 929989, 1273927, 2978315, 536581, 446505, 954561, 1421485,
			938021, 1298461, 1102075, 3002835, 643179, 561165, 4059141, 2339303, 192525, 3150023, 4059645, 733203,
			790707, 2281545, 2830995, 1077261, 2453821, 2085265, 1896611, 807085, 4625487, 2510915, 1298605, 1503465,
			1134759, 741477, 6115525, 192549, 1282317, 3977413, 397343, 3609453, 1724495, 569357, 1380383, 815231,
			1913143, 1765603, 2527569, 1814727, 413755, 733227, 708735, 3961463, 733189, 462957, 520229, 864365,
			446469, 536613, 2756627, 3592809, 610365, 3388135, 126983, 1077357, 2756621, 1257713, 6190003, 1773635,
			3027225, 5771301, 1028127, 8532021, 2454051, 782433, 3076289, 3510309, 1569061, 2773585, 1593475, 2281921,
			2757029, 1355855, 4543107, 1052755, 2650117, 2363565, 1429851, 987237, 1642647, 340029, 5010237, 4182633,
			4232055, 929905, 913421, 1626201, 2675301, 1110255, 1282325, 1593475, 2429419, 2240549, 1773899, 1724483,
			667659, 2306053, 1159275, 1052725, 3100725, 1282061, 2429239, 2331087, 3879795, 2306239, 913455, 2871567,
			3166591, 790719, 1765489, 3371451, 2797611, 610315, 2330713, 2756627, 4305725, 2535603, 1871913, 2011525,
			4297587, 4059993, 1593615, 2871669, 3043869, 1503459, 438303, 1052691, 4174507, 2330671, 2625607, 1421341,
			2674801, 2363585, 1716573, 2281821, 5402803, 2510907, 1503321, 2699877, 4452579, 929919, 929797, 290827,
			667719, 1765437, 684051, 569457, 2429419, 913451, 1716327, 3150015, 2535987, 987237, 167949, 569453,
			1429635, 4256571, 1077459, 1626305, 1765773, 2453733, 2240685, 3519191, 864309, 446469, 2945307, 790607,
			3076529, 2486529, 2216219, 1274149, 2462127, 684103, 2699575, 2830745, 2215949, 3027543, 930015, 1773849,
			987287, 5279749, 1298745, 2215983, 1052709, 1429635, 4379033, 3313827, 2904171, 1675575, 2142587, 3264523,
			4083903, 364627, 1527947, 3043789, 364561, 741513, 1355829, 1675323, 741473, 438277, 3609085, 2707527,
			2142471, 1626243, 643079, 1159401, 1527881, 733267, 1552641, 2707899, 3805935, 954535, 979177, 1839121,
			1675305, 2339109, 2625759, 3903561, 733215, 4002123, 3117409, 1888593, 929959, 2462007, 1110077, 643151,
			3371011, 1159257, 3732027, 2044283, 1552403, 536587, 1593625, 2904243, 1445917, 4477961, 2830997, 4355045,
			167953, 1675445, 438375, 2510909, 4133685, 4969067, 2462183, 2535845, 4378763, 1568791, 1503525, 3395603,
			2011141, 1355987, 4223167, 979143, 913547, 2084953, 1552697, 667695, 937995, 364549, 1888519, 643223,
			4305363, 741533, 733333, 5231049, 1872095, 667707, 569471, 4297675, 4026985, 2773593, 3371027, 1896629,
			3609267, 3371681, 1429617, 1052703, 290883, 1994789, 1896905, 1446055, 667761, 1994765, 241675, 1675307,
			1470705, 643151, 1150989, 2756757, 3437283, 806955, 5411693, 69643, 1675575, 2363661, 1716283, 2331181,
			913413, 6386697, 4722915, 1765437, 2134519, 1642735, 1773581, 782373, 741515, 1642885, 3265125, 94221,
			1888609, 249909, 1110273, 2486381, 987173, 569403, 69637, 2240541, 3363463, 1429677, 2142575, 864357,
			2404551, 3223949, 2240579, 2527689, 2011153, 2699347, 1134849, 1552427, 954591, 3977707, 2699457, 4862053,
			3395957, 2453943, 4575585, 806925, 2707467, 1355799, 1257621, 561193, 2634207, 1913205, 1912935, 1814877,
			3608889, 2404501, 1798371, 1593405, 1380635, 1962015, 1626159, 1282259, 364597, 1503543, 2978511, 2044181,
			5157343, 118803, 1257705, 1429617, 1995141, 3903861, 5116293, 290883, 1200145, 1814547, 1028163, 1839477,
			987327, 2871627, 733257, 5255845, 929845, 2085121, 1421341, 684103, 1626429, 1134595, 3879001, 1527821,
			741525, 807069, 5034723, 3510277, 2511059, 2240849, 3617037, 1798461, 1503443, 2142407, 2830517, 413763,
			4837975, 6541541, 1151173, 1101951, 241693, 2945035, 397343, 1675323, 241711, 1568781, 1257635, 2060415,
			4354157, 1913061, 1200319, 807015, 299045, 1380531, 4083759, 1355885, 6787899, 733189, 520205, 1716475,
			2011233, 438369, 4231589, 1200259, 1282331, 741435, 4599819, 2871447, 274479, 684045, 569357, 4133793,
			5845591, 2904453, 2945527, 2011317, 1642585, 3436547, 2134473, 2486315, 3510873, 1765599, 5329573, 2240913,
			5231025, 2142545, 3371585, 1814569, 1282215, 2535443, 1446037, 1626171, 1470471, 1814961, 4149795, 610443,
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			2830937, 790551, 1257585, 4026889, 1200397, 1503245, 684189, 1568865, 1134723, 2707955, 2511245, 929919,
			3150365, 3166311, 1052725, 1298643, 2429017, 1896555, 3223925, 2331181, 2633825, 45059, 1470727, 2060635,
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			2085055, 1593367, 4986019, 987333, 938123, 1995135, 1356083, 4084679, 397359, 1773839, 3002939, 667689,
			421977, 421907, 1028329, 782437, 1052733, 1257713, 978981, 954429, 1421401, 2461709, 3518493, 1421325,
			684159, 4256027, 790569, 2338913, 815123, 3879169, 1913181, 1446027, 1273859, 1421569, 3265099, 1814835,
			241669, 2707517, 1470697, 1298671, 1101927, 2707889, 2773285, 3388039, 2699647, 1110183, 2084971, 2904255,
			2945527, 2797705, 3838419, 1593367, 1052733, 3314407, 2281803, 2240793, 864275, 2634341, 1298493, 3764577,
			1356083, 1200135, 536605, 1429571, 790691, 1593445, 2584595, 3633973, 462885, 1134759, 1994993, 1445917,
			1675365, 3117327, 299019, 733281, 1798317, 5435759, 249869, 3510585, 1872183, 1151203, 1552715, 3076247,
			438351, 561265, 1380533, 249863, 2527333, 5239091, 1798301, 4625171, 4149601, 569481, 520239, 1355805,
			1814565, 2134209, 1724763, 1839145, 77835, 3265251, 2830979, 4346475, 2462237, 1872321, 1528071, 3436647,
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			561169, 1798575, 1765759, 299051, 2978021, 151581, 3265245, 520245, 2625735, 2527411, 3904309, 1380405,
			1724805, 1273959, 2650263, 2830395, 1814791, 397379, 274437, 2527515, 4026831, 1052677, 3732063, 413733,
			1814679, 708651, 3608935, 913461, 2625853, 1274049, 1896671, 1110021, 1527921, 1626141, 643085, 3960999,
			790707, 929931, 2486631, 684159, 520215, 1298445, 2011603, 2904483, 2945155, 2363541, 192531, 1995105,
			2330865, 618557, 1134689, 1798425, 3224073, 536685, 741449, 6271685, 1962297, 610375, 1503255, 2339249,
			1962255, 2486843, 3264685, 1380563, 1421409, 3027587, 2060301, 364585, 3764487, 1896681, 1446127, 1028185,
			2085213, 1355939, 1028209, 610405, 2134425, 413755, 2486319, 733281, 4862131, 1102065, 815241, 4296985,
			1257765, 2331133, 1814635, 708775, 1077477, 1110257, 2084973, 3117789, 2363723, 1257485, 3224001, 1773725,
			4059359, 667751, 4133771, 2044035, 569381, 643109, 1593607, 2044017, 2429091, 3150563, 323587, 610417,
			2060385, 1626141, 2584809, 1814929, 1912989, 1282161, 1888273, 3977529, 2904069, 2060767, 5157297, 462859,
			929949, 561165, 1077499, 1150989, 5952035, 413709, 1077309, 815163, 2527321, 4838173, 1274055, 3879631,
			5845005, 2486763, 1888467, 9286131, 2306061, 1101853, 2535495, 1626117, 1642843, 2363741, 1896471, 2142711,
			2798185, 339981, 446477, 1896837, 1421625, 3002439, 2707461, 864413, 2707805, 1626251, 1257575, 2945107,
			5042403, 1028133, 5624931, 2674729, 323645, 741503, 3027027, 1102065, 1814841, 4886709, 1716285, 2404355,
			1839133, 2904171, 806949, 536589, 5239091, 1626261, 913535, 3149829, 1773599, 1200159, 3511095, 1503315,
			3076757, 2625807, 5280091, 1159317, 290845, 340029, 4084071, 2585177, 2461809, 536629, 462927, 1765647,
			1282311, 1552403, 2904741, 2584985, 3960945, 1110063, 2044127, 1470523, 1765723, 2363493, 2633741, 782467,
			806955, 340021, 1642515, 864437, 2797899, 2773435, 3101069, 2584845, 1798493, 2527399, 151583, 3903729,
			2584869, 610323, 340005, 2904605, 1470747, 1724699, 3321885, 3100911, 3977715, 2044215, 815133, 954595,
			3493925, 1421623, 790533, 1052883, 1839373, 2142617, 1724775, 2486499, 708745, 643085, 643199, 3322119,
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			1593471, 2707935, 1200319, 2060685, 1962333, 1593507, 2060347, 610315, 3608589, 2011623, 1995111, 2625819,
			1257729, 3977703, 176135, 667785, 610323, 2756711, 2634107, 1724693, 1552403, 1626501, 807079, 1274107,
			3150483, 2527599, 4518639, 1110153, 1913065, 3854547, 3117109, 4174221, 1839513, 569381, 1052701, 2699371,
			438279, 782353, 1888483, 2535555, 2084887, 2486535, 1642575, 2756801, 1257699, 5575143, 1134605, 4027287,
			3362845, 708655, 1814617, 2453947, 3535467, 1568857, 815207, 2461953, 5312775, 1552595, 3117765, 1528089,
			299011, 1962295, 1470553, 2134213, 421955, 3150075, 1052689, 2339279, 3322503, 1569039, 1445971, 1257513,
			1675541, 741555, 987139, 3166441, 1839331, 1593601, 1593577, 1028113, 1716253, 4174633, 2511455, 2633967,
			1028335, 7737405, 3764963, 667659, 2904147, 6271245, 4379645, 6434821, 1028205, 1421355, 978973, 2044263,
			2945391, 3838301, 2363669, 913509, 5313509, 815301, 536599, 929973, 1642557, 1716465, 2527483, 53251,
			1569147, 2142717, 3166885, 1470573, 3608613, 2216445, 1200175, 1052895, 987179, 4354067, 3617367, 1470505,
			643145, 6099183, 1888527, 2977863, 987149, 2011243, 815297, 2707529, 167943, 2084937, 2650405, 1814821,
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			610365, 3101021, 249867, 2675179, 1151115, 1962081, 1642735, 1052839, 1872261, 1446195, 397379, 1773573,
			684169, 929973, 929797, 1896641, 438375, 782463, 954475, 9410035, 3166477, 913437, 1101865, 1912873,
			520197, 2216063, 2339363, 1052799, 1110209, 4182239, 3150137, 2142357, 684049, 954561, 1716355, 2142407,
			520205, 2535653, 536647, 2527489, 339985, 438355, 2216217, 1675437, 3101363, 1773699, 2871427, 2363913,
			1593703, 929931, 3731865, 520205, 3150003, 938165, 1994793, 2330857, 2281669, 2511215, 3878943, 364591,
			1642879, 3805825, 864323, 3002531, 1593351, 610309, 2527399, 618509, 782367, 1134633, 1552697, 2756925,
			2060445, 1429773, 1077471, 610365, 1839283, 2011141, 2674999, 176169, 1527921, 3314131, 3903645, 6320787,
			3002651, 2428933, 2461763, 1839231, 1134629, 2429125, 5042343, 1765605, 1724423, 2511119, 2281959, 1273929,
			2363603, 4182837, 3608649, 2281669, 2011519, 2486873, 4083969, 3764451, 2404389, 5116283, 2306449, 1110249,
			1150987, 684139, 126995, 1028193, 2625693, 790691, 3518567, 1429661, 2511021, 1773647, 782367, 5403231,
			569349, 520239, 3371577, 1101921, 667653, 929991, 151555, 938163, 1028143, 3609153, 1429701, 5411703,
			2043941, 1675277, 2240819, 3494615, 1593711, 1355939, 1773761, 4296915, 5952509, 3535467, 618605, 446469,
			1077411, 815115, 421893, 5869573, 249875, 561223, 5034055, 708645, 4026825, 815177, 3076287, 561195,
			3117093, 1642579, 462901, 2011159, 569441, 2044067, 1765587, 118807, 741389, 118789, 3960963, 1298541,
			1798293, 364557, 561225, 1872095, 290847, 1724459, 1871901, 3166959, 1101925, 192519, 1282329, 1257695,
			1429727, 3879831, 3731637, 2011485, 1101963, 2011293, 397395, 1593543, 1626275, 5330125, 69645, 3395627,
			249893, 2044235, 3026967, 4599999, 1716291, 2798109, 249885, 3854923, 929829, 3592461, 1052743, 1798491,
			2756613, 4354179, 2085177, 2650309, 2044173, 299045, 2773005, 2707635, 954507, 1159407, 2675257, 4763905,
			1159349, 1569075, 1257609, 397325, 1298503, 3436645, 1429617, 1552623, 3117699, 1716265, 340041, 1159341,
			2674869, 2830485, 536673, 2142561, 1200265, 2429155, 1675595, 1798511, 1994795, 2798175, 1724517, 1839463,
			864365, 2404357, 569357, 1724655, 8303365, 3535581, 954541, 1888293, 340047, 2240621, 1593381, 1888527,
			1675343, 520221, 3494475, 618645, 782475, 397325, 2904641, 2486315, 1675377, 569445, 1765477, 1568869,
			4084091, 323643, 1912995, 536689, 4304933, 1356045, 2281533, 4494231, 1626213, 2904105, 1503489, 1101975,
			462931, 2429001, 1282061, 741555, 462927, 643209, 3223593, 2773623, 4862065, 4862553, 397315, 4297651,
			2625727, 3436861, 5575717, 4305269, 3879849, 3608619, 217131, 6959535, 806941, 413707, 438361, 1052901,
			2330857, 4469713, 2306319, 708759, 1888485, 1724435, 536635, 1159445, 1077429, 1798407, 520205, 1773965,
			1798545, 4223139, 3715173, 151575, 1814569, 3027515, 1839435, 1888527, 1282107, 3117325, 4887625, 1282119,
			1470757, 1110033, 3535015, 3854757, 790691, 1503341, 2240679, 2797831, 2085355, 3027081, 2511357, 864357,
			1872185, 4354077, 3166501, 1888453, 274455, 290821, 3043417, 2535605, 1159401, 339981, 708757, 2535615,
			2527735, 2330991, 323601, 3608959, 618597, 176139, 274475, 1101829, 3535491, 741407, 1077315, 2461947,
			1642833, 9171237, 684093, 954579, 2510945, 3633729, 274437, 3518505, 978991, 1028115, 561211, 249897,
			1470663, 618645, 2707613, 4059375, 1913293, 1773809, 1159341, 2707583, 53253, 1552731, 241695, 1282317,
			667779, 6812669, 2429211, 2060731, 1282239, 782515, 1765639, 4256553, 4838283, 733293, 3322533, 536599,
			4149267, 1773627, 1724429, 4002469, 2773015, 1569117, 929893, 2306095, 1724699, 3100761, 2142225, 3371219,
			299013, 2945733, 8655707, 364605, 1445917, 1642855, 684189, 708771, 1888273, 3854803, 1273861, 1298673,
			1273917, 1421541, 1527915, 610317, 176139, 2584955, 2404509, 192549, 1675413, 741503, 2486579, 69637,
			1355817, 708697, 4797507, 2330653, 1101883, 1839477, 3510333, 2675287, 569373, 1273863, 1282305, 1839277,
			1626149, 446505, 1134783, 176147, 3616869, 815133, 2363519, 1724825, 4624493, 1773801, 2486813, 1552481,
			1568931, 1298683, 610341, 1134653, 1200285, 1421365, 1773629, 2404785, 807063, 2773393, 741393, 569381,
			1593537, 1274149, 6582285, 536599, 2756615, 1773765, 1773881, 1134629, 3027435, 1273861, 2142629, 733321,
			1626461, 979101, 790587, 2281503, 3616875, 2977919, 339979, 1200279, 421971, 2535435, 929859, 978949,
			364605, 3395763, 413763, 3518703, 1159331, 1159221, 3838265, 1912837, 1839175, 3592749, 2306247, 979053,
			1077285, 987245, 979005, 782473, 1773845, 2281753, 2904671, 1421625, 2134077, 462951, 2675085, 1724469,
			2044001, 2338845, 1552607, 4256321, 561193, 1257743, 3117457, 2584613, 733231, 1380635, 2338905, 741379,
			2215949, 3903987, 954579, 6639953, 864345, 1888437, 1028253, 1134663, 733245, 2363481, 1028143, 643211,
			2240615, 339991, 1110147, 4600035, 3100935, 643131, 1421539, 1380381, 1569085, 2404549, 2281545, 1994979,
			2756955, 937997, 4625195, 1200265, 610401, 446477, 1724795, 2511015, 364567, 987363, 1716297, 446469,
			1626155, 1257621, 4862065, 1552457, 2904531, 4919753, 339991, 2650633, 4920035, 2060301, 3395765, 5402895,
			462907, 3854883, 2011533, 3043333, 1257611, 954421, 864405, 2404357, 3002531, 2584827, 733203, 684115,
			3609303, 1282079, 413719, 413749, 4969055, 667709, 1527957, 1962165, 3076605, 987173, 2536011, 4149901,
			1995219, 1675317, 520205, 3313875, 3363363, 2331081, 1962051, 1134773, 987225, 1159437, 1274005, 610383,
			1765379, 1159187, 1102053, 1896761, 1429533, 864423, 3264517, 1134605, 2904131, 536649, 2486775, 3715791,
			618575, 1765755, 4231677, 667679, 1962135, 4149631, 4026937, 1773669, 2511335, 2281893, 2904297, 364563,
			3027537, 1134693, 421901, 1159401, 1962147, 1896495, 1503275, 1380395, 1913253, 1470477, 1503495, 1675353,
			1200165, 3731875, 1716537, 1527821, 3371781, 4256691, 2650117, 397365, 610341, 3117729, 643221, 618567,
			6664593, 69637, 1765617, 126981, 4297213, 1503381, 1839157, 4026549, 1273869, 2454013, 2904473, 954457,
			1298521, 643133, 2429295, 1798407, 561175, 1052839, 1896561, 1626201, 1429661, 4231625, 4468987, 4543233,
			1839505, 3100779, 5009647, 5870181, 3314011, 340015, 2527503, 618537, 561189, 1298535, 1626309, 1101865,
			610407, 1839207, 3150387, 1839261, 4452615, 733189, 3100709, 1028325, 6116311, 2404893, 5895157, 2134069,
			1446159, 1773585, 2339013, 2461835, 241669, 6435247, 2797881, 4002249, 299069, 708747, 2453905, 3805771,
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			3363255, 1356003, 929931, 1257519, 1077267, 1429535, 2134059, 987225, 1159331, 643151, 979155, 610393,
			2871753, 1896659, 126993, 2134449, 2363453, 1798343, 1445985, 1716297, 806995, 4133651, 1896765, 1429533,
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			4304903, 618509, 421931, 1470591, 3854607, 2216033, 413709, 987287, 536659, 1282091, 4477629, 2707955,
			2281561, 913601, 561169, 1675277, 2404395, 806959, 1798575, 1626143, 6418443, 569385, 1962427, 610315,
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			741459, 2240619, 3616959, 6091821, 3150197, 2085211, 3371045, 2511117, 1470601, 3265165, 4862629, 2306355,
			4575845, 462931, 1273929, 1839451, 806973, 1429737, 1298665, 299025, 2461923, 954421, 4231187, 864335,
			1716303, 3765021, 2453607, 340039, 4133835, 6435577, 1814565, 1446051, 446477, 2462175, 274437, 2707569,
			520221, 1675337, 3854683, 929811, 1896453, 987141, 1421395, 1298715, 126989, 569385, 2142245, 2011285,
			1298469, 2331085, 4543345, 3903549, 569447, 290883, 1528049, 929931, 3322565, 790617, 1962097, 5280205,
			610347, 167973, 987147, 1298701, 1872035, 2134029, 864315, 1675515, 1159199, 323657, 954517, 3608649,
			1257683, 1724835, 1568857, 1896821, 1528085, 2699353, 299067, 3715685, 954475, 782515, 3002831, 807019,
			1814541, 5771371, 1028099, 864309, 438333, 938025, 290829, 1052751, 4518579, 397335, 1151253, 4296835,
			3264679, 1888293, 708621, 217105, 421901, 2674995, 1798317, 1773735, 2011447, 299061, 1110057, 2830767,
			1355913, 3002391, 1552403, 151569, 3027107, 1380461, 3076665, 561157, 2011159, 1200139, 913467, 3592203,
			1421325, 1814865, 979057, 1355877, 954595, 1872165, 4083851, 2707977, 1274139, 1446019, 8204445, 1134615,
			2363621, 741399, 733281, 4543431, 2584995, 3396023, 241677, 2281483, 1773627, 2675025, 913521, 815241,
			1110125, 3609433, 2330637, 2699455, 323597, 4886709, 421893, 4346083, 1872303, 3961551, 3223565, 6788201,
			1134701, 1593615, 1552641, 2306247, 3150563, 913497, 3387835, 167973, 241701, 2330647, 1380395, 1773819,
			274491, 1274089, 5829267, 4150167, 2134479, 1552395, 2429157, 2142225, 2363453, 2404929, 2084877, 3731835,
			520259, 536605, 929835, 2486859, 2306385, 954415, 954447, 2830937, 2338863, 708675, 1773747, 1896759,
			1888609, 2978031, 1052719, 2363853, 2511045, 1593675, 2871613, 1273893, 569397, 1446171, 610347, 1798281,
			1151007, 790691, 364557, 2511389, 6345477, 520203, 782409, 1765725, 1568799, 2486795, 3043485, 4715307,
			1527861, 1814877, 1871973, 3764901, 2773233, 4518535, 2142459, 241711, 1282061, 1380365, 2142627, 1773875,
			1552743, 3494195, 2011555, 2011597, 2084893, 413737, 3076427, 462931, 1257555, 1872269, 6090931, 2634087,
			2871783, 3879091, 1503269, 610401, 2626123, 864437, 2085237, 2978283, 790533, 274473, 1273965, 4059375,
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			2773183, 323621, 2060425, 462921, 2535731, 3002937, 3026981, 4493731, 2625999, 3223679, 1626471, 618623,
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			1814557, 2428981, 815201, 438303, 536595, 1888527, 979107, 1159367, 2527299, 3044005, 7672901, 3043875,
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			2797759, 782475, 3592431, 864429, 339991, 2756919, 1642729, 1839513, 806973, 782439, 2134389, 2044035,
			4920393, 1151043, 1913103, 2585043, 3043501, 3002499, 2707583, 1470621, 1527869, 1913083, 2060467, 2625885,
			1642659, 151581, 3977943, 2216357, 4026717, 1429577, 864369, 2339123, 4862613, 1765555, 3265075, 1871889,
			3002651, 4001829, 1896881, 4083819, 929941, 667731, 290883, 1429677, 3224261, 1257629, 1159215, 1716237,
			2429359, 2461755, 1429521, 1200361, 782355, 1052845, 4379343, 3510925, 1569085, 1380603, 1380635, 1200199,
			954565, 3117085, 1716229, 2281993, 364591, 2773191, 3387453, 1896687, 2240703, 1257699, 4797009, 741479,
			6272205, 1642719, 2634075, 987365, 1503579, 1642509, 249875, 1765465, 1102005, 954469, 2527569, 806991,
			2674881, 3855145, 1568773, 1356033, 1552647, 1134653, 4715323, 438313, 1528115, 2085093, 1773905, 708681,
			4133001, 1134701, 2404813, 1151073, 3264559, 2486333, 274449, 2773359, 1888261, 3838565, 1470553, 1503591,
			806955, 2240525, 806935, 3322469, 1282175, 340009, 1642845, 1421359, 3371661, 1913221, 2699811, 1077295,
			2043909, 1872321, 1159397, 6099311, 954475, 1503333, 2363643, 1151133, 1642509, 2756715, 438343, 446469,
			913455, 2707895, 5009461, 3043707, 3608773, 1421371, 1913101, 2011473, 413701, 2043947, 2134167, 929971,
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			1159181, 938007, 69645, 2429235, 569471, 733245, 708615, 618537, 790571, 438315, 2626057, 3314277,
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			4231775, 954561, 4174635, 1257701, 4231761, 1356087, 536629, 815127, 20483, 1282149, 2871343, 1134633,
			3223751, 790547, 2978469, 569451, 1298661, 1077267, 1159419, 7647237, 2011245, 2527501, 1077319, 2871309,
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			4624395, 2650729, 413703, 2650479, 4714533, 3765063, 3371441, 2330635, 806925, 3101313, 2363831, 1765587,
			782443, 3731595, 249863, 3961379, 1552665, 5928171, 864435, 3027563, 2044365, 741389, 1421421, 2339247,
			1716255, 1765573, 3363603, 1872071, 3592229, 3837965, 3117193, 1773669, 708735, 2461703, 979081, 4624397,
			1151215, 1724435, 790629, 1151089, 1798307, 3633553, 3322047, 2281891, 2675235, 1101837, 1552395, 2510885,
			4624425, 1429821, 5656833, 217135, 1282221, 1052773, 1814809, 1159347, 3100811, 3166231, 1839141, 1962235,
			6344811, 5829029, 618579, 1527849, 241701, 2675167, 2945511, 1503339, 2330721, 5730783, 2339087, 5256135,
			807015, 2773665, 1257509, 643119, 3616979, 3395597, 520209, 1102035, 1626125, 1528079, 1773735, 1200357,
			1200339, 782341, 1355837, 3617565, 2462159, 1962183, 4297087, 4625241, 1528047, 5288873, 6272225, 815145,
			2756747, 2978151, 1962393, 1110189, 1356057, 2085265, 2044323, 274493, 3264525, 2363913, 643085, 2404365,
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			2511267, 1077265, 217105, 7566483, 3265213, 2454051, 2134437, 5256255, 2363405, 1626309, 176165, 1503413,
			708669, 1274029, 2085211, 3043437, 1503255, 618579, 462889, 364615, 790701, 2331057, 4133247, 2044011,
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			1503383, 929865, 1552737, 3313671, 397323, 1159265, 2527513, 987237, 569451, 1962013, 1913253, 3395931,
			1429775, 643125, 1724469, 1773839, 929865, 1527957, 249875, 1716303, 1134609, 2142587, 4796639, 2462163,
			806925, 1724769, 1110119, 3002981, 3903819, 2044361, 192525, 5042927, 1593717, 5337131, 1077471, 446483,
			1528031, 536595, 3117807, 1716243, 1200277, 708687, 1421485, 77829, 151583, 2240555, 2486303, 1528115,
			299037, 2634065, 1052733, 3395597, 4149949, 1839109, 979011, 3608949, 3362953, 397373, 1429667, 684169,
			1380355, 1716501, 2281933, 790617, 3371681, 5067395, 323627, 1961997, 438303, 2216025, 3592631, 2011555,
			167967, 3510385, 3633259, 610387, 7689925, 1200399, 1028167, 618593, 2536001, 1798355, 643079, 2306061,
			249887, 1839315, 4150219, 2306437, 1675277, 2773015, 1626293, 2675131, 421925, 1470547, 561219, 913475,
			4256253, 1593447, 684195, 2650683, 1995035, 2461739, 421901, 3387765, 954427, 2830359, 1626191, 643185,
			1773591, 1298605, 2281993, 1872129, 2240979, 2339379, 3117697, 733195, 1470613, 4797569, 1028139, 6116071,
			1765503, 1912933, 1871933, 1028259, 2134165, 4494381, 290829, 2453535, 3616877, 1445949, 2453755, 2240961,
			561259, 1355957, 4001923, 2216267, 2339319, 1257501, 1110021, 421911, 806925, 1912935, 3633163, 1151245,
			2945655, 954457, 806955, 413709, 1298529, 340041, 1028277, 2699527, 741485, 4453085, 2773579, 3961169,
			364557, 299025, 733189, 782499, 1913143, 643199, 3314437, 1077285, 4354407, 1380381, 2707835, 4886799,
			2338821, 438279, 610341, 1052905, 1151115, 667671, 1716481, 4133775, 1626443, 1134825, 1355967, 1355829,
			1470745, 733311, 2044263, 684133, 3166827, 1446117, 2241033, 3609207, 1503389, 5854365, 413743, 1568949,
			2404423, 3608713, 2650461, 3264679, 2699821, 2945733, 667715, 978951, 1872045, 929805, 1593495, 1765645,
			2904227, 741381, 1716495, 339981, 397355, 290869, 4182293, 618509, 4002553, 1273879, 1077399, 667749,
			3117487, 2330637, 741527, 2330677, 1568865, 299021, 741405, 2044187, 1888587, 5312553, 1626305, 569447,
			2707979, 1724607, 1527915, 1716561, 1814959, 2634045, 1642579, 2674827, 1429507, 364605, 643091, 2142357,
			806943, 3101051, 77837, 913535, 929931, 5869825, 561205, 913413, 1642843, 2453607, 4518745, 2773513,
			6828723, 6090951, 1282245, 274461, 733341, 2945107, 2797609, 4838163, 3715283, 913515, 815187, 274469,
			446553, 2535777, 1028101, 3264789, 1675535, 4255797, 1552541, 413725, 2650393, 1765633, 684171, 3265021,
			2486619, 987329, 569349, 2044293, 6091693, 643199, 1593613, 2363915, 2527429, 2363781, 2625999, 1470661,
			1724433, 2240615, 1159299, 3002681, 1593441, 2830599, 2338979, 2650381, 2461797, 118787, 2633891, 2240643,
			176169, 1814617, 3437313, 118789, 5411409, 913445, 3715911, 2585007, 1962405, 782409, 2216129, 2585055,
			2511089, 2633829, 299011, 364551, 1724555, 1995219, 2330637, 5353981, 1380405, 667653, 807103, 1298529,
			2871727, 2404579, 938055, 790571, 4518117, 3322413, 1200157, 2306481, 1773759, 290839, 2527549, 413709,
			1994789, 807019, 1446015, 2363789, 1814533, 1872165, 1593613, 2142381, 1257651, 5009571, 1593571, 2011149,
			1716535, 2756891, 1994783, 2634237, 1077475, 413733, 1962081, 1839417, 2339339, 2216319, 1773699, 1298437,
			1077477, 1888413, 2461719, 782341, 1380593, 290835, 1470487, 2527471, 741447, 1282085, 3977287, 1355987,
			2585039, 2011317, 1962021, 2454081, 4231737, 1814779, 2674699, 684163, 290853, 2216043, 3117613, 1839115,
			1888699, 1273915, 1872071, 5853683, 741381, 3879529, 2945677, 3265119, 1626275, 815211, 1052829, 3117267,
			610365, 741389, 2650125, 1429787, 3493935, 249909, 2428995, 339999, 3166885, 2871727, 2241053, 610365,
			2625729, 1273965, 364581, 3362847, 864383, 643185, 7992849, 815151, 3117687, 2240541, 274491, 45061,
			6025785, 708667, 4346509, 2306245, 6362379, 2625853, 1798511, 323651, 667661, 462885, 561205, 1200157,
			3224123, 3731605, 3977673, 1028307, 2134437, 2306109, 2011239, 2330703, 3518531, 1028319, 1429697, 1257711,
			1052695, 2044235, 274437, 2429427, 1912845, 176159, 815187, 1151199, 3002787, 2699457, 1274035, 561163,
			2527321, 815127, 4132881, 2240775, 2707535, 1552389, 2871903, 536617, 2142237, 2011147, 3437331, 1773837,
			1077337, 1798377, 2536041, 1642777, 561213, 1134819, 2330977, 913425, 2142491, 1470535, 3494219, 954457,
			806953, 1102017, 421901, 2461719, 561165, 1995003, 3978169, 1159251, 5043393, 2904663, 3608845, 643143,
			1134863, 2339057, 4624737, 2043963, 1593453, 1355873, 2584959, 929943, 561157, 1839373, 2585177, 741555,
			913559, 618609, 1282161, 667757, 1716505, 1527957, 2511117, 938141, 1593451, 979051, 1773731, 1028185,
			1101895, 782349, 1282187, 3805195, 2134227, 643221, 684105, 2330797, 954381, 3518565, 1274113, 3027171,
			462879, 1839255, 462879, 569475, 3960905, 667787, 1445961, 2281555, 4133465, 1552455, 2240991, 3223691,
			339979, 1298545, 2134435, 2084947, 1839145, 1273893, 4378629, 2134437, 3617459, 536673, 2281599, 3322127,
			1552389, 618519, 2699347, 4797567, 3371727, 708681, 1421461, 438277, 217131, 1470595, 1839115, 913469,
			1871951, 536599, 3043815, 790545, 1896647, 1716285, 3002961, 1642833, 3371279, 1134741, 1642677, 2338965,
			2306199, 2674711, 5034625, 2085063, 3313687, 684069, 733293, 3633843, 3616785, 987203, 2904657, 1110125,
			2527275, 610417, 1200277, 1626345, 2773243, 1962211, 806949, 2650551, 2707527, 1593427, 5574897, 2363669,
			1355837, 2404515, 1995201, 364623, 1134681, 3715077, 1593571, 1298505, 126981, 1912999, 5288747, 1200199,
			3961251, 1765489, 806917, 241677, 3076155, 4968629, 3608713, 1134605, 438303, 4887247, 561265, 667655,
			1151043, 3838779, 1257711, 1814575, 913413, 1716583, 913589, 1470481, 2871309, 1200231, 4150135, 954525,
			299019, 1159391, 1298625, 2461853, 2281915, 938151, 1101927, 1765557, 3100809, 3879529, 4223245, 3879685,
			1380663, 1724525, 1593661, 2281741, 3535221, 2977805, 397331, 364605, 1675293, 1888495, 1282149, 1159247,
			2773005, 5574757, 2634315, 2085261, 561283, 2871609, 929875, 1470691, 938177, 3322575, 1028329, 5402895,
			536617, 5239605, 5435849, 708687, 1552563, 2142279, 3494561, 708759, 1626261, 1151113, 2871783, 1724529,
			561165, 978967, 536643, 5730393, 2699877, 1356015, 1888629, 3518721, 2535773, 1077499, 4084179, 561171,
			733189, 2675331, 2363955, 3764517, 1913145, 978967, 1421379, 1159229, 3633799, 2142617, 1912891, 2060367,
			1159227, 2331003, 2633865, 167949, 3117369, 290819, 6115417, 1134759, 3314307, 1298485, 1421451, 2904341,
			1101871, 708771, 151565, 4600355, 2584847, 1569105, 1429841, 1962337, 2281603, 3903871, 1429761, 1257531,
			421961, 733195, 2510957, 1994865, 1872185, 2142345, 421947, 1871979, 1765653, 3715781, 2216163, 2240999,
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			167949, 1298451, 2675187, 1568775, 4305249, 2486565, 4084019, 3764261, 2215949, 954499, 2871859, 1052821,
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			5231631, 2339097, 1273969, 815285, 1077415, 1626221, 1298437, 1642773, 1912939, 913509, 446481, 1626141,
			4223619, 340005, 323651, 1077487, 421955, 1593405, 1839107, 2535587, 2584655, 3715841, 3518885, 1888687,
			782353, 1716447, 3101415, 2773539, 3510429, 1839283, 1814835, 2634275, 2240969, 249859, 3027635, 1274085,
			1101855, 1151035, 249909, 2453655, 4256555, 1257723, 2060565, 1355835, 2527291, 2453695, 2699293, 1896905,
			1593567, 929829, 1151157, 1528085, 323613, 2011387, 1077277, 610405, 5157811, 3494081, 1642563, 1716583,
			2338899, 2216207, 4861957, 1257653, 462895, 1102017, 241695, 1110197, 3002981, 536617, 7059005, 2134213,
			1896639, 2699445, 2134123, 4001919, 2281645, 929983, 4354641, 2240861, 806931, 1429787, 1200207, 1994963,
			1273861, 3076575, 2044043, 4084283, 1675577, 1896807, 1503263, 741435, 684037, 446571, 2216133, 913413,
			5066915, 1527935, 2904335, 3002547, 446561, 1913215, 1470733, 2585189, 1028137, 2773365, 1765387, 3371639,
			2084875, 1527897, 708717, 1052913, 4133321, 2707647, 290821, 2699743, 1445917, 2535863, 2330647, 1429515,
			1913163, 790589, 569391, 4026717, 1110069, 3117709, 4576053, 2453545, 1839213, 741459, 2707773, 2044115,
			929859, 3395973, 339987, 1552389, 3223555, 241693, 913479, 1552737, 3363549, 1798205, 167965, 3322665,
			3510523, 3854437, 1052773, 929805, 4476947, 3592631, 4182963, 1421421, 2535615, 2306241, 2772997, 733245,
			2462033, 684045, 1962333, 3149895, 3313977, 569375, 1724835, 1503411, 1896779, 1995185, 94213, 929865,
			1151043, 1503395, 929839, 4002103, 1355999, 1282299, 4624925, 3166435, 2674861, 1995089, 938057, 815187,
			3977617, 2453613, 913475, 2904165, 249875, 2453785, 3633363, 1773879, 708621, 2060371, 1528155, 3223683,
			2142489, 462853, 4297743, 1724517, 462855, 4059197, 1052733, 118797, 2339093, 1446169, 1110119, 864369,
			6115495, 2338827, 176159, 3960921, 274493, 1626221, 2945113, 4149999, 1798205, 4231269, 2404699, 1151157,
			1282161, 438351, 1282107, 1446145, 3117313, 1429797, 217091, 2797807, 4133057, 3510523, 1675271, 3879279,
			2674845, 1355885, 339979, 2134465, 610335, 5772087, 4231359, 2625883, 1355913, 2044077, 340047, 1593711,
			3264871, 118795, 806941, 2142365, 1626305, 2216037, 2945595, 2011155, 192523, 2486379, 1773831, 2044083,
			708615, 2240585, 2339283, 2281525, 2461845, 176133, 1773767, 610375, 3731889, 1716351, 1200379, 1642653,
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			1421413, 1913199, 1503455, 5116637, 340021, 2240595, 1995185, 1200139, 2331021, 913605, 3002625, 3961379,
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			1716505, 2871799, 1642725, 790655, 1355817, 954411, 1765473, 4452945, 2707767, 7696511, 2306109, 1503291,
			2338853, 1724457, 1814937, 3396045, 446531, 4837843, 815127, 1446205, 1110143, 1888677, 610375, 1569081,
			1470795, 4182413, 151583, 2486451, 3363073, 1028139, 3100965, 2060377, 815277, 2625579, 2871447, 3224183,
			684129, 397349, 610357, 1028259, 1282197, 1159307, 3437197, 1773921, 1470775, 364581, 1675631, 2675149,
			2240585, 2282013, 2142219, 241681, 913557, 1421593, 561199, 1642509, 364549, 4297651, 643145, 3224313,
			3076727, 2773483, 2756771, 3436581, 2708075, 1994769, 3264891, 1077487, 249859, 1200141, 5411769, 741555,
			167973, 708705, 4346515, 643085, 1273965, 610363, 1355885, 1110095, 3387901, 364549, 1593375, 1110123,
			610309, 938181, 938177, 1724525, 1257639, 806979, 1724583, 1626491, 3518925, 1871895, 290859, 1872311,
			1257663, 3732049, 913619, 2085045, 290869, 1355885, 954439, 1552613, 1273885, 2142459, 1282145, 413707,
			2043917, 2060671, 3166561, 1282151, 364563, 3322205, 1642693, 3731895, 4026439, 4354689, 3617207, 299045,
			421893, 1257723, 954525, 1888513, 2904215, 2404383, 446469, 2527695, 1421421, 1150999, 979005, 3265263,
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			1593651, 3027507, 3396087, 643115, 1077385, 2584605, 569447, 1052911, 438345, 2142437, 929959, 741473,
			3617355, 1298739, 4714539, 733257, 2699455, 4355019, 987287, 643077, 708721, 2461965, 1839147, 2756957,
			1110267, 1028263, 1134603, 1052713, 2240643, 2756747, 3592197, 1257515, 610417, 2699269, 782449, 1102023,
			1716495, 1724699, 2675235, 5156935, 2215983, 2404405, 3265213, 1552757, 929859, 3519147, 217131, 561157,
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			77829, 2216213, 1773707, 4919909, 1593441, 1896821, 610309, 1552397, 2338889, 3101355, 1888675, 954421,
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			3224013, 2461977, 1273939, 561169, 2584617, 364623, 1994925, 1282359, 708681, 2675127, 2486319, 4231527,
			1200133, 815145, 1716277, 1298589, 6345413, 3314227, 569349, 1896545, 741435, 2306197, 3519165, 929859,
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			2060467, 2240663, 3715745, 3043981, 1470747, 2871367, 2404735, 1077261, 4174191, 5035005, 1355907, 1995021,
			1110125, 815255, 1994933, 2756891, 364627, 2085351, 364627, 979137, 2773305, 1101981, 1871975, 569423,
			94221, 561163, 249909, 1626351, 741513, 1962451, 1134803, 561235, 1421335, 5927085, 987263, 929919,
			1994951, 1200309, 2707889, 1429541, 1724553, 3314407, 1110087, 1298515, 1503543, 3396201, 2044335, 929851,
			536703, 3519275, 1159229, 3166687, 3731947, 790541, 643179, 5329993, 2756921, 929797, 4837389, 2674887,
			1446039, 1503335, 815145, 929929, 1257509, 1798227, 937997, 1798157, 1724615, 1568821, 2650579, 1429655,
			446487, 2453893, 643209, 3609235, 987245, 2085087, 618605, 2084977, 2486373, 3321917, 4968795, 1642623,
			438277, 782415, 339999, 815135, 1765389, 1814839, 2338877, 4378691, 2404503, 1159251, 5895295, 176169,
			1298563, 3616875, 708765, 77837, 5845075, 1527981, 667731, 2134153, 987315, 1110207, 3510513, 938063,
			2331013, 3387853, 1896537, 1527915, 954465, 421931, 536589, 1429613, 4182105, 1028107, 2134033, 2830725,
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			741473, 806979, 2306185, 815207, 2404549, 2338823, 1503525, 1593697, 5951525, 2585183, 2527305, 2904131,
			864395, 217099, 2281581, 4059155, 2429337, 2978213, 462907, 3534997, 938013, 1839301, 913497, 3166519,
			782463, 561165, 667785, 2085045, 1569039, 2830877, 1913065, 2306107, 1421469, 3494565, 3387619, 1200411,
			1872009, 4132953, 643119, 3223973, 938055, 1134623, 2142687, 5944005, 913413, 4354749, 3592869, 520215,
			1724447, 741395, 1052743, 2871363, 708619, 1765555, 126989, 151569, 4084649, 1134609, 1052709, 1716261,
			3313765, 2142627, 2306589, 1568941, 217131, 733197, 1150979, 667779, 5952371, 3264543, 2707887, 1675373,
			1077253, 2585097, 1724733, 3519065, 3879333, 782355, 2904741, 1355957, 1134731, 536647, 53259, 1380603,
			1159221, 1896857, 2044197, 807079, 2306145, 1765525, 2142665, 1101981, 241677, 4027009, 3314205, 536635,
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			2281873, 3837957, 1110267, 1913029, 2429389, 2830757, 2633817, 1675365, 1110167, 913509, 708765, 2511389,
			987333, 3903601, 2756639, 3076109, 2216315, 782463, 176139, 4133133, 3043695, 2134021, 2797675, 4256777,
			618515, 4149517, 3322617, 1200159, 2584893, 815109, 1798415, 1994865, 2306059, 1765399, 364627, 1151083,
			1159407, 1503321, 2134327, 2699415, 1257765, 1675317, 3396285, 1798493, 2363423, 987189, 561165, 1356003,
			274437, 1527975, 2871969, 1429671, 446477, 536623, 3395663, 2134507, 1962415, 3166221, 1642653, 1994765,
			4862011, 2945127, 3764313, 3314205, 1912855, 1642663, 340041, 413749, 1470615, 708721, 4059999, 2363703,
			1872293, 3362955, 2142335, 2756717, 643155, 979075, 290869, 1470601, 2904231, 3437001, 2871979, 1101973,
			4838029, 1200157, 1134731, 2527719, 979101, 2633741, 3593015, 4862005, 1429817, 4493349, 2330763, 1626309,
			1814701, 2633879, 6639827, 4600829, 1888275, 421941, 1134699, 610413, 2650389, 1568869, 2461733, 4256165,
			446477, 1912905, 4084395, 1503585, 1913221, 1528115, 3715613, 2527695, 4575585, 2084923, 3100685, 2871463,
			1912915, 1839123, 3044029, 3977785, 2084877, 667787, 1814811, 5894317, 462871, 1298451, 929805, 708613,
			1765449, 2085195, 643145, 1675361, 290839, 667761, 3395711, 1626339, 446525, 4493709, 1765429, 3633535,
			2044337, 2461709, 782349, 1052869, 1134611, 3313927, 733237, 667691, 2674851, 2134413, 3519137, 1724477,
			1356009, 618509, 1527845, 6590483, 5657133, 2363913, 397323, 2978249, 1568947, 1527999, 708627, 217107,
			815183, 3838301, 1569105, 5256261, 2404609, 1962367, 2134465, 1446099, 2625903, 1110029, 1355829, 2797669,
			1257701, 708771, 733273, 2011215, 1151239, 1871915, 1962301, 643179, 1626215, 4920287, 2338839, 1593483,
			978957, 5067615, 2134213, 1593475, 3043435, 987285, 2708027, 1134815, 2650339, 4084481, 2011419, 2797731,
			2216109, 1913061, 1356053, 1913271, 1626125, 684073, 2945641, 2404459, 6639885, 3166317, 708625, 2707517,
			290845, 446505, 807093, 2486715, 4379487, 2085001, 2945697, 438313, 3101021, 1503549, 2240525, 1429737,
			4002291, 2216117, 2511395, 462861, 979111, 1528089, 397355, 2306595, 2453617, 938043, 790571, 3388093,
			1569105, 1470475, 1527815, 2904431, 1765465, 1798481, 1995021, 2830653, 1429761, 1052677, 2330665, 561219,
			2584619, 2363541, 1675361, 241701, 2331147, 2134257, 1052839, 2535737, 7811109, 1298743, 3314257, 1028197,
			1150987, 2142651, 2084973, 1995099, 3805893, 864261, 2011143, 2281485, 4001823, 1675535, 2486781, 323615,
			2904083, 192549, 937995, 3854349, 3592245, 4985319, 340047, 913559, 1101865, 118789, 815213, 790685,
			2945623, 1028227, 1913289, 1798147, 2536001, 77829, 2330857, 340005, 323613, 2535987, 3314053, 1503539,
			790665, 2363585, 3609037, 1528065, 1814685, 1716487, 979101, 643133, 684103, 930015, 5034703, 3363007,
			2633765, 5354755, 1102035, 2216015, 1282107, 938123, 438303, 1446045, 1888467, 1552653, 667685, 2429199,
			1962315, 1995209, 2428941, 1200133, 3117183, 1593373, 1101897, 4920215, 643131, 3494331, 1642509, 4001805,
			1798385, 3519111, 4026429, 3166407, 2281971, 4797363, 3044001, 2871955, 4002619, 1446111, 1773669, 1380551,
			2134213, 1675325, 1380371, 978991, 1773879, 3535141, 1470747, 323601, 2486511, 1888489, 864363, 2453857,
			1077459, 4378713, 2625573, 2830359, 5009781, 2044263, 1839415, 1675613, 864363, 667661, 1298715, 815141,
			241687, 1552427, 1568881, 126999, 1568829, 2699811, 1503525, 618537, 3518655, 290821, 3387451, 610333,
			2871949, 1569079, 1642515, 2011245, 1298725, 397349, 5600223, 1765435, 2363855, 1814907, 1642575, 3715245,
			1814761, 1716613, 3321995, 2306215, 290847, 323595, 3388153, 1028275, 979155, 618593, 1839151, 274463,
			1101975, 2626107, 1593691, 1962015, 3314437, 733335, 815241, 929949, 1773671, 1503411, 2011375, 569417,
			2510859, 299015, 2625687, 1814929, 397329, 1552511, 954567, 20483, 3314143, 3166539, 3715125, 1724769,
			2535915, 1273987, 1200235, 5009505, 151565, 3371157, 2871775, 1159295, 2044031, 53253, 1110125, 1380593,
			733341, 446505, 3436825, 3166669, 2756711, 3633835, 274451, 643103, 1446201, 2773651, 397383, 1896509,
			979005, 1159181, 1159305, 618579, 413707, 1257561, 708625, 4625435, 1470661, 520203, 536643, 3101373,
			708759, 1298445, 3387499, 5034847, 2060401, 3117465, 1593637, 5730825, 1421619, 176141, 979141, 2216367,
			1962241, 3511095, 1675665, 126995, 1257579, 1888513, 1134731, 1150989, 929881, 536629, 4797477, 2462079,
			2330685, 1446087, 987153, 53255, 708687, 929971, 954565, 806971, 1552577, 1110033, 1552697, 1298493,
			2240793, 2510999, 618633, 1962393, 397355, 1159205, 2281555, 4346497, 3960905, 815121, 2584713, 684189,
			864259, 2511185, 3535201, 2633837, 2453517, 69637, 2306155, 1765587, 1724595, 1052709, 741443, 929803,
			1569075, 1626117, 2084967, 1200339, 2707463, 1814677, 2404923, 2060419, 2535873, 3592715, 2707517, 1527971,
			340005, 2699613, 176141, 2330907, 1503455, 954495, 954519, 1642527, 5338319, 610357, 1773765, 5828801,
			2142437, 1200309, 1257555, 2306319, 3363589, 2871649, 1298435, 1282215, 5034031, 2461715, 1642777, 782347,
			5402751, 1552565, 1101885, 2060461, 28677, 1077477, 1134833, 1380531, 1798241, 3838595, 2281699, 1995045,
			3838629, 2011467, 1355843, 1626383, 2216367, 1101841, 1134719, 217099, 2240955, 3101031, 815147, 2585039,
			2281515, 979075, 1503509, 1552515, 979111, 1380363, 561195, 1839297, 2142371, 3879039, 1077295, 1429613,
			987225, 1765387, 1470477, 1798211, 6271167, 1896515, 446493, 1298671, 2773065, 2945355, 1839171, 1110045,
			1872293, 1282077, 1200231, 1282187, 462861, 2306437, 1888275, 4182083, 1421569, 684045, 3322497, 1765605,
			2625799, 1445947, 2330857, 3043681, 1642567, 536593, 397349, 1102065, 3223845, 5157433, 2773053, 938165,
			1445959, 1159229, 929845, 1470613, 1257669, 1355781, 4256663, 1298491, 1839381, 4297501, 1110105, 45061,
			1724553, 217091, 815267, 1077379, 1298473, 274491, 1593697, 913421, 1872179, 2486721, 1872185, 1503269,
			2429025, 3715473, 4468903, 5952737, 1257525, 1716325, 864285, 864279, 667679, 2535755, 1110195, 4723709,
			299061, 667799, 741407, 2011417, 1159439, 2216285, 1151173, 1552541, 6951051, 1527947, 569475, 987245,
			364573, 1200319, 1896645, 2240553, 569391, 1110285, 741389, 1765485, 1052853, 929845, 274445, 397317,
			438285, 979005, 913545, 397343, 806983, 864363, 987369, 2043975, 4059533, 561231, 2584757, 1593585,
			1527897, 2871403, 1528019, 2281485, 2060291, 421901, 1282061, 1593607, 3494355, 2306119, 299013, 1429671,
			3166261, 1552665, 667667, 2871873, 241669, 3044001, 3518747, 1159445, 2904173, 987147, 2084961, 1962363,
			1626309, 2977889, 397355, 913581, 815267, 1077385, 2453905, 2584589, 3002721, 569481, 1888383, 1470507,
			3150263, 3371781, 1872291, 3076619, 1298511, 2306589, 339999, 2633867, 2584677, 3265105, 1527825, 1380465,
			2757041, 864315, 3313743, 2339013, 1159395, 413707, 2453641, 2085195, 2461793, 2044175, 5854505, 5239541,
			249909, 708621, 1077327, 69645, 1380355, 2511207, 913427, 2634315, 610393, 2633835, 3149975, 1134849,
			3592793, 1380621, 1675377, 2330863, 3027317, 3076727, 2216399, 741443, 397371, 5771361, 397373, 3732049,
			536665, 2625853, 864345, 1593415, 3166407, 1445935, 2707805, 2044145, 1962021, 3117657, 1298715, 2634111,
			1716463, 1568865, 3100839, 1429695, 3166545, 1257533, 954409, 3879469, 53253, 446501, 1569127, 5354383,
			1527813, 299025, 1913293, 413779, 815297, 1913179, 1298631, 3510651, 364627, 1282319, 987335, 3002717,
			1962135, 1470561, 1028185, 1052745, 929853, 1503305, 2404773, 1028307, 3519095, 438343, 3960893, 1995161,
			618567, 299069, 3396005, 1839493, 741407, 3518691, 2084887, 217117, 274455, 4027227, 978957, 536589,
			1798233, 3592793, 5338175, 4723817, 1913095, 4518879, 2945581, 618569, 2085171, 3027185, 3002735, 913421,
			4468815, 979041, 1445925, 1028115, 1028289, 2060647, 618507, 1298715, 299045, 1675283, 2453611, 2306221,
			2904485, 5599723, 1134689, 53255, 3371601, 3510373, 2650423, 864303, 4715593, 667661, 1798541, 561231,
			4083995, 1421623, 815253, 3436953, 979081, 741435, 1445907, 3903765, 2306281, 446507, 1429601, 1110147,
			4379511, 2454051, 3100899, 2584995, 2674747, 1724555, 987369, 2011287, 249915, 3224213, 5312571, 4518067,
			2707767, 979071, 438303, 3494181, 667785, 1052863, 2044133, 741381, 3363265, 1527965, 643185, 1716231,
			2363741, 462957, 643209, 569387, 3117087, 2511141, 2011363, 1626461, 1110027, 1724795, 323631, 1642729,
			2511395, 569373, 3437005, 520245, 1675269, 2675331, 1110045, 1159449, 2043951, 1110119, 913431, 741419,
			741417, 1151199, 1159197, 1445895, 667805, 987327, 2429469, 1470577, 4231229, 667695, 2626099, 1912959,
			2830757, 2363429, 3510277, 864383, 561213, 2011387, 1470525, 1257753, 1839175, 3436701, 1159305, 536659,
			913481, 413727, 3076335, 1380581, 290875, 3043609, 413763, 1421493, 1568967, 2945601, 249861, 3027183,
			929985, 1675541, 1552467, 1298665, 1552715, 4494003, 413715, 1626155, 807075, 364627, 2338829, 3166671,
			929805, 2330961, 2011405, 2535777, 1257653, 6386277, 954579, 1626123, 1470577, 3633289, 2699487, 299055,
			4173861, 3494519, 1798197, 6542193, 3731959, 1552511, 1200235, 413703, 1527813, 3715833, 1896461, 4223737,
			1028325, 2216147, 2404839, 2142251, 2625663, 1528041, 2060671, 1839303, 4149439, 2338875, 3395963, 2216439,
			2584727, 2216375, 2330847, 536617, 1077261, 1568829, 1102017, 2945091, 618527, 340009, 1052899, 5575389,
			1626131, 2707613, 1298563, 2486471, 3978163, 684093, 1552701, 3437143, 2085061, 708645, 2486409, 7001125,
			3518661, 1200139, 462859, 3076697, 3322509, 299069, 1724649, 1527975, 4518709, 3715901, 176141, 413709,
			4173925, 3166287, 1257683, 2404783, 249915, 446505, 3002735, 45061, 1888363, 569411, 2650675, 2462045,
			1642603, 5329069, 2142357, 1913215, 1569051, 1814757, 462859, 643131, 1257513, 1888437, 1994985, 1077405,
			2535665, 1888533, 217093, 217101, 1470603, 684129, 733267, 938097, 2011467, 462879, 2043907, 1552455,
			2650683, 987293, 1552443, 3903729, 667689, 929835, 708765, 1913265, 1896587, 536649, 815115, 4723179,
			4002019, 708687, 807021, 938175, 3731553, 1593723, 1274007, 217095, 782373, 2060709, 561211, 979141,
			3314037, 1503501, 2486339, 2584599, 2338839, 2633807, 3371685, 2404405, 1716481, 1642827, 1429583, 643101,
			3223703, 5337105, 3322149, 1077349, 1110155, 2707461, 2830923, 1888323, 2011503, 6829431, 782341, 610309,
			1814565, 1552407, 2511389, 987219, 2240541, 2338833, 1298439, 3977263, 1765633, 2404753, 1814637, 1446015,
			1273897, 2625589, 2674695, 2044347, 937995, 3854365, 2011315, 1445907, 1528101, 2486849, 806925, 3371171,
			1159449, 2330721, 6271727, 3879505, 2904117, 1077309, 53253, 3371579, 1962333, 1151005, 2363703, 610323,
			2625667, 1962295, 1274037, 3264691, 1101837, 1994949, 1872273, 2757009, 1995003, 2330635, 1421365, 954477,
			2060619, 708687, 4346097, 3101159, 2486693, 3027585, 1872189, 2142245, 2215959, 3854779, 5575357, 806973,
			2363853, 1872063, 8163885, 1839231, 3166389, 3043395, 520253, 1724835, 1642779, 708775, 2978181, 167965,
			806923, 2527245, 1593405, 5976711, 6026073, 807063, 5280315, 2830907, 299039, 3609139, 1839355, 151583,
			708747, 4059905, 2011143, 2626035, 3854425, 1077265, 4223569, 2330775, 1470801, 2216117, 2281951, 1470595,
			561183, 815123, 1626491, 241705, 2085093, 3535077, 4796709, 2675319, 3395993, 1962427, 438343, 1429733,
			806991, 2756991, 864395, 4305317, 2011245, 1528139, 1200295, 192549, 1839471, 6665451, 1896785, 1913211,
			1552613, 2060619, 2404855, 929971, 2535813, 1077259, 2634305, 1569037, 3731565, 806959, 2708063, 2363463,
			3838145, 2674881, 340039, 1200259, 643143, 2462055, 1273929, 520271, 979107, 1913023, 3224001, 929991,
			1257735, 2699811, 2708043, 3264711, 1552697, 1151205, 364581, 2707697, 5288115, 1773957, 1282067, 643101,
			462861, 1552437, 4797519, 3879225, 438289, 3002381, 2404489, 1798293, 1273927, 2633979, 167955, 1151037,
			864293, 1446225, 2306079, 2585183, 1839441, 561235, 69645, 2585009, 1593537, 3117505, 3101181, 806929,
			1052731, 2904707, 2510951, 782397, 2977803, 1429797, 4453401, 3879529, 1380533, 1273869, 1568797, 1896837,
			684121, 2584977, 274493, 2757267, 1888467, 1814805, 1200225, 2339373, 1380663, 1052803, 2044145, 1527891,
			618533, 2281651, 2339133, 192529, 1724765, 1159445, 1151083, 937989, 954547, 5034235, 2977929, 2060707,
			438319, 2461725, 2404551, 954379, 1773881, 2044167, 2797699, 2044383, 2134125, 2429025, 3264823, 2461947,
			3264955, 2011443, 1675617, 2060779, 1994759, 2011273, 1110021, 782467, 1052821, 3593013, 3027491, 1994925,
			2043963, 3076515, 438303, 2798029, 954373, 5239893, 987315, 741483, 1355795, 1273897, 3387673, 1716261,
			3854433, 2625769, 176165, 1765669, 438309, 667757, 929895, 1839543, 741465, 438277, 2453557, 2338905,
			2134189, 520239, 6190207, 1470517, 1200237, 2978139, 1872165, 2240693, 610335, 1675461, 3117129, 1642869,
			1871883, 978963, 2134209, 1773597, 3633745, 5067521, 806983, 1716261, 979041, 2798139, 1380411, 1110167,
			864323, 684075, 5337531, 3396395, 1110249, 1077429, 2240669, 2634161, 241717, 1503369, 2634177, 53253,
			3313669, 2584707, 1470469, 610311, 2429337, 1593601, 790637, 1282229, 1528035, 1110147, 1896509, 2060511,
			3592271, 6812037, 2486343, 1814629, 1912845, 2486529, 708669, 733333, 323589, 1872035, 3731965, 3436813,
			421911, 1429517, 1257701, 2142515, 2830775, 2282019, 2461907, 5287989, 2339109, 1200217, 815163, 708619,
			1527813, 3592461, 979093, 1159437, 1257485, 1159235, 1962087, 1257515, 2084905, 1724435, 1888335, 364623,
			782433, 569349, 667755, 2060439, 1716603, 2871613, 1962057, 53253, 708621, 2830967, 1839115, 3150581,
			708621, 667737, 2511371, 2707517, 151563, 938015, 2773173, 1593423, 1765515, 1675637, 5035047, 1445997,
			3322469, 2011225, 1257729, 618525, 2429209, 1101853, 1429835, 77837, 2757255, 1445925, 4182897, 1675647,
			1765617, 2404365, 1675305, 3518471, 1298475, 446525, 2142359, 6606877, 2363793, 1962381, 3076485, 782517,
			2486399, 1503431, 2060331, 4149561, 1896641, 1282187, 937997, 815109, 6812445, 3592949, 2306527, 618549,
			2453821, 790659, 1257663, 5010091, 790539, 2428995, 3027545, 3608619, 3715935, 4493943, 4493815, 733267,
			4575243, 4354905, 1528157, 2535587, 2978025, 1134821, 1528001, 4059293, 1568829, 979027, 1028169, 2134021,
			2871369, 4575237, 1159187, 151565, 5600553, 815133, 733207, 1429523, 2404449, 2773453, 2363801, 684133,
			3715901, 864261, 2060479, 4182749, 815217, 1470705, 413715, 274455, 3534919, 1380591, 2306077, 2461923,
			446469, 6952201, 290847, 413749, 561255, 3535335, 4173981, 1200285, 3076689, 2461887, 3223619, 610347,
			8082501, 2429329, 77837, 6419093, 2650569, 807103, 1110075, 667685, 2215973, 1200139, 741483, 1798241,
			413715, 2904215, 3854587, 3633913, 2060775, 1994755, 2404785, 520233, 1765599, 1724565, 1503245, 1888413,
			2510867, 3961169, 1552641, 708679, 733215, 1503489, 1421409, 1356059, 4862229, 413701, 151565, 290821,
			1380533, 1028289, 3715781, 2527389, 151555, 782353, 782485, 954481, 1503585, 2633747, 2535771, 3732225,
			1429737, 3903541, 1421379, 5239661, 1200411, 520233, 1470507, 2453617, 2453565, 5288999, 3027293, 1888423,
			2134447, 151581, 2453797, 618509, 1773671, 2462159, 2338845, 807019, 2404453, 3076485, 1994771, 299015,
			2330905, 3002457, 5035023, 987177, 5034631, 3265131, 3117733, 3076749, 1470703, 4084521, 2339169, 3371741,
			1528157, 1962403, 1503303, 1200307, 3805651, 1716331, 176141, 1896549, 1257651, 2011515, 2708075, 2453913,
			1298437, 782347, 2240849, 2306199, 2011483, 3396335, 1102063, 3362965, 2453653, 4083795, 249899, 954507,
			1912903, 1421395, 2241015, 1151043, 3960921, 6238717, 2338845, 1110063, 3387501, 618501, 520251, 536629,
			4452983, 1110039, 684163, 643169, 3395637, 815201, 1527989, 3633925, 1077345, 2306247, 1593615, 2535653,
			1273993, 1527935, 3387465, 1110239, 5402733, 2363429, 684135, 2339097, 1839397, 1134639, 3633573, 3224199,
			4296711, 618557, 4232087, 864329, 3313815, 536581, 1716333, 3043851, 569475, 1429731, 938097, 413785,
			3101009, 1642753, 684181, 3436707, 1200391, 610321, 6140001, 1839385, 3371021, 1470757, 1429547, 1871939,
			3100899, 1962165, 1028113, 3396033, 2699871, 2084877, 807085, 2461709, 1200139, 1134671, 339981, 3224129,
			1527811, 2044137, 1421349, 1896455, 2085261, 2945403, 3166275, 4223985, 3879489, 1470691, 5238921, 2306115,
			2338869, 3076443, 1593601, 6665745, 3027563, 2584827, 1568773, 413733, 2511159, 1134783, 987149, 1773665,
			1159229, 610377, 2633817, 667677, 249887, 1569135, 1274127, 94221, 2650285, 1716267, 5255631, 1446067,
			2134153, 151581, 364627, 1159395, 3371681, 806917, 1626501, 1994943, 1052733, 938157, 4714687, 1429835,
			3117093, 1159407, 3633595, 2306397, 1159331, 2043909, 2240625, 323613, 2084869, 1380419, 610311, 1355907,
			3592301, 1159359, 2215967, 249867, 1421491, 176159, 462955, 4223895, 618549, 462921, 5313129, 2634081,
			1962385, 3854629, 5574849, 1446165, 2363643, 3043585, 1355805, 3265033, 643075, 987219, 561279, 2330773,
			167941, 3838349, 2674881, 176157, 3592305, 610365
		};

		// given 0 <= a,b,n < 2^64, computes (a*b)%n without overflow
		inline uint64 safe_mul(uint64 a, uint64 b, uint64 n)
		{
			return (boost::multiprecision::uint128_t(a) * b % n).convert_to<uint64>();
		}

		// given 0 <= a,b,n < 2^64, computes (a^b)%n without overflow
		inline uint64 safe_exp(uint64 a, uint64 b, uint64 n)
		{
			uint64 res = 1, pw = 1;
			for (int i = 0; i<64 && pw <= b; ++i) {
				if (b & pw) res = safe_mul(res, a, n);
				a = safe_mul(a, a, n);
				pw <<= 1;
			}
			return res;
		}

		static bool is_SPRP(uint32 n, uint32 a)
		{
			uint32 d = n - 1, s = 0;
			while ((d & 1) == 0) static_cast<void>(++s), d >>= 1;
			uint64 cur = 1, pw = d;
			while (pw) {
				if (pw & 1) cur = (cur*a) % n;
				a = ((uint64)a*a) % n;
				pw >>= 1;
			}
			if (cur == 1) return true;
			for (uint32 r = 0; r<s; r++) {
				if (cur == n - 1) return true;
				cur = (cur*cur) % n;
			}
			return false;
		}

		// given 2 <= n,a < 2^64, a prime, check whether n is a-SPRP
		static bool is_SPRP(uint64 n, uint64 a)
		{
			if (n == a) return true;
			if (n%a == 0) return false;
			uint64 d = n - 1;
			int s = 0;
			while (d % 2 == 0) { s++; d /= 2; }
			uint64 cur = safe_exp(a, d, n);
			if (cur == 1) return true;
			for (int r = 0; r<s; r++) {
				if (cur == n - 1) return true;
				cur = safe_mul(cur, cur, n);
			}
			return false;
		}

		static bool IsPrime32(uint32 n)
		{
			if (n == 2 || n == 3 || n == 5 || n == 7) return true;
			if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
			if (n<121) return (n>1);
			uint64 h = n;
			h = ((h >> 16) ^ h) * 0x45d9f3b;
			h = ((h >> 16) ^ h) * 0x45d9f3b;
			h = ((h >> 16) ^ h) & 255;
			return detail::is_SPRP(n, detail::bases32[h]);
		}
	}

	namespace Math
	{
		bool IsPrime(uint64 n)
		{
			if (n <= UINT32_MAX)
			{
				return detail::IsPrime32(static_cast<uint32>(n));
			}

			//if (n == 2 || n == 3 || n == 5 || n == 7) return true;
			if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
			//if (n<121) return (n>1);
			if (not detail::is_SPRP(n, 2)) return false;
			uint64 h = n;
			h = ((h >> 32) ^ h) * 0x45d9f3b3335b369;
			h = ((h >> 32) ^ h) * 0x3335b36945d9f3b;
			h = ((h >> 32) ^ h);
			int b = detail::bases64[h & 16383];
			return detail::is_SPRP(n, b & 4095) && detail::is_SPRP(n, b >> 12);
		}
	}
}
